Derive Lovelock Gravity from String Theory in Cosmological Background

Understand

It was proved more than three decades ago, that the first order $\alpha'$ correction of string effective theory could be written as the Gauss-Bonnet term, which is the quadratic term of Lovelock gravity.

• In cosmological background, with an appropriate field redefinition, we reorganize the infinite $\alpha'$ corrections of string effective action into a finite term expression for any specific dimension.
• This finite term expression matches Lovelock gravity exactly and thus fix the couplings of Lovelock gravity by the coefficients of string effective action.
• This result thus provides a strong support to string theory.